Many medical students enjoy their paediatric attachments at undergraduate level but aren't so certain that they want to do this as a career that they are ready to sign up for the training programme to start at the end of FY2. If you do, great....but check out the page on applying for paediatric training here. Also take a look at some advice from the LSoP recruitment subgroup on how best to apply.
Others feel like they need to explore the speciality a little first and want to spend some time in a clinical fellow or "FY3" role first. There is a wide range of these in most specialities in London. These are not set up by the RCPCH or Health Education England, rather locally recruited and funded by individual trusts. Most will appear on NHS jobs.